Image quality of the computer-generated holograms are usually evaluated subjectively. For example, the reconstructed image from the hologram is compared with other holograms, or evaluated by the double-stimulus impairment scale method to compare with the original image. In previous research, we proposed image quality evaluation by peak signal-to-noise ratio and diffraction efficiency. Theory and numerical experimental results are shown on Fourier transform transmission hologram of both amplitude and phase modulation. In this paper, we compare objective evaluation method and subjective evaluation and verify validity. Subjective evaluation is performed by optical and numerical reconstructions, and objective evaluation is performed by the structural similarity index and diffraction efficiency.

Image quality of the computer-generated holograms are usually evaluated subjectively. For example, the re- constructed image from the hologram is compared with other holograms, or evaluated by the double-stimulus impairment scale method to compare with the original image. This paper proposes an objective image quality evaluation of a computer-generated hologram by evaluating both diffraction efficiency and peak signal-to-noise ratio. Theory and numerical experimental results are shown on Fourier transform transmission hologram of both amplitude and phase modulation. Results without the optimized random phase show that the amplitude transmission hologram gives better peak signal-to noise ratio, but the phase transmission hologram provides about 10 times higher diffraction efficiency to the amplitude type. As an optimized phase hologram, Kinoform is evaluated. In addition, we investigate to control image quality by non-linear operation.

We have investigated the floating image display, which named computer-generated alcove hologram. The viewing angle was enlarged by changing the shape of the computer-generated hologram from flat to semi-half cylinder. To employ the calculation method of the computer-generated rainbow hologram, the full color floating image which has the wide viewing angle is reconstructed. Since these computer-generated holograms have the wide viewing angle, the correct hidden surface removal method is required. <p> </p>In our previous work, the computer-generated hologram was calculated by using the large number of object data from different viewpoints. When the fringe pattern was calculated, the calculation area is divided into small segments, and each small segment is calculated from one object data. The reconstructed image of the computer-generated hologram should not show the hole or overlap on the different viewing position. The small segment needs the several viewpoints information, especially the reconstructed image is close to the hologram plane. Therefore, the reconstructed image of the previous computer-generated hologram is concerned about the possibility of the hole or overlap. <p> </p>In this paper, we have proposed the improved hidden surface removal method which uses the virtual window. The calculation area, which is determined by the virtual window, is added to the object data. To apply the improved hidden surface removal method, we have achieved the more correct reconstructed image.

We have investigated the floating full color image display with the computer-generated hologram (CGH). The floating image, when utilized as a 3D display, gives strong impression to the viewer. In our previous study, to change the CGH shape from the flat type to the half cylindrical type, the floating image from the output CGH has the nearly 180 degrees viewing angle. However, since the previous CGH does not have wavelength-selectivity, reconstructed image only has a single color. Also, the huge calculation amount of the fringe pattern is big problem. Therefore, we now propose the rainbow-type computer generated alcove hologram. To decrease the calculation amount, the rainbow hologram sacrifices the vertical parallax. Also, this hologram can reconstruct an image with white light. Compared with the previous study of the Fresnel type, the calculation speed becomes 165 times faster. After calculation, we print this hologram with a fringe printer, and evaluate reconstructed floating full color images. In this study, we introduce the computer-generated rainbow hologram into the floating image display. The rainbow hologram can reconstruct full color image with white light illumination. It can be recorded by using a horizontal slit to limit the vertical parallax. Therefore, the slit changes into the half cylindrical slit, the wide viewing angle floating image display can reconstruct full color image.

We have been developing direct fringe printer that can output holographic fringe on a photosensitive material. The pixel pitch of the printer is 0.44 micro-meter and the printing speed is 3 gigapixels per hour. Although the speed is faster than that of other printing methods, more speed is desired to print over 100 gigapixels holograms. In this paper, we use high power laser to reduce the settling time that is required to eliminate vibration after a stepper motor movement. Some other improvements are also discussed.

The hologram is known as the ultimate 3D display because it has all three-dimensional information and the reconstructed image of the hologram provides the natural spatial effect. It has been demonstrated that the laser hologram or the photographical hologram can record and display a 3D image as real as the object is existing there. There have been many researches to realize such realistic 3D images with digital holograms. However, required pixel number for the practical 3D digital hologram is much higher than that for 2D images. Therefore, fast generation of computer-generated hologram (CGH) is quite important. This paper reviews recent progress on CGH, mainly done by the author's group. In addition, output methods such as holographic fringe printers and holographic video displays are also reviewed.

A computer-generated hologram (CGH) is well-known to reconstruct 3-D images faithfully, and several CGH printers are reported. Since those printers can only output a transmission hologram, the large-scale optical system is necessary to reconstruct the full-parallax, full-color image. As a method of a simple reconstruction, it is only necessary to use a volume reflection hologram. However, the making of a volume hologram needs to transfer the CGH by means of an optical system. On the other hand, there are printers that output volume type holographic stereograms with the full-parallax, full-color image. However, the reconstructed image whose depth is large gets blurred due to the insufficient sampling rays of a 3-D object. The authors propose the volume hologram printer to record the wavefront of a 3-D object. By transferring the CGH that is displayed on a liquid crystal on silicon, the proposed printer can output the volume hologram. In addition, the large volume hologram can be printed by transferring plural CGH that recorded the partial 3-D object in turn. As a result, the printed volume hologram has been able to reconstruct a monochrome 3-D image by white light illumination, and realized the full-parallax image.

The floating 3-D image, when utilized as a 3-D display, gives a strong dimensional impression to the viewer. Few researches, however, have been conducted on the floating image display by means of the computer-generated hologram (CGH). Since the required pixel pitch is narrow compared with the non-floating image display, the CGH that displays the floating image could hardly be output. If the CGH is output by the device with insufficient pixel pitch, the viewing area and image size of the CGH are not suitable for practical use. Therefore, the object is usually placed behind the hologram to relax the pixel pitch. Reducing the time in calculation is also required. The authors have been developing the fringe printer, the device for fringe patterns, which can be reproduce holograms with the pixel pitch as fine as 0.44 μm. This study investigates the fabrication the floating image display, which is output by the fringe printer, with wider viewing angle and larger image size. It is clear that the image is necessarily reconstructed by the conjugate of the original reference wave to reproduce the real image.

A computer-generated hologram (CGH) is well-known to reconstruct 3D image truly, and several CGH printers
are reported. Since those printers can only output a transmission hologram, the large-scale optical system is
necessary to reconstruct the full parallax and full color image. As a method of a simple reconstruction, it is only
necessary to use a volume reflection hologram. However, the making of a volume hologram needs to transfer
a CGH by use of an optical system. On the other hand, there are the printers which output volume type
holographic stereogram reconstructing the full parallax and full color image. However, the reconstructed image
whose depth is large gets blurred due to the insufficient sampling rays of a 3D object. In this study, the authors
propose the volume hologram printer to record the wavefront of a 3D object. By transferring the CGH which
is displayed on the LCoS, the proposed printer can output a volume hologram. In addition, the large volume
hologram can be printed by transferring plural CGH that recorded partial 3D object in turn. As a result, the
printed volume hologram has been able to reconstruct a monochrome 3D image by white light, and realized the
full parallax image.

Recently, researches on digital holographic 3D display are getting very active as well as the digital holography
for 3D image acquisition. This paper reviews recent research activities in Japan, including digital holographic
3D video displays, digital holographic fringe printers and computer-generated holograms. The holographic video
display includes 100 megapixel full-color full-parallax display, horizontal scanning display, enlarged viewing
angle display. For the fringe printer, laser plotter and tiling systems are introduced. For the computer-generated
hologram, various kinds of hologram types are described as well as fast computation methods.

In this paper, we have investigated the floating image display with the computer-generated hologram (CGH).
As the 3D display, to make strong impression on the viewer, the display should reconstruct the floating image from the display plane.
However, there are few reports about the floating image display with the CGH.
Since the required spatial frequency to the display is very high compared with the rear image display, it is difficult to output the CGH which display the floating image.
If the CGH is output by the inadequate device, the viewing area and the image size of the CGH is limited.
Therefore, to reduce the required spatial frequency for the fringe pattern of the CGH, the position of the object is placed at the behind of the hologram plane.
Also, the huge calculation amount of the fringe pattern is a big problem.
In our work, since we developed our output device (named fringe printer) for the fringe pattern, the pixel pitch of the printed fringe pattern achieves to 0.44 &mu;m.
By using the fringe printer, we have obtained the floating image with the CGH.
The output CGH can reconstruct the floating image, but the reconstructed image only has the narrow viewing angle and the small image size.
To make the wide viewing angle floating image display, we investigate to change the CGH shape from the flat type to curved type.
Also, to solve the huge calculation amount, we employ the GPU for parallel calculation to make the computation faster.

In this paper, we have investigated the floating image display with the computer-generated hologram (CGH).
As the 3D display, the floating 3D image gives strong dimensional impression to the viewer.
However, there are few reports about the floating image display by the CGH.
Since the required spatial frequency to the display is very high compared with the non-floating image display, it is difficult to output the CGH that displays the floating image.
If the CGH is output by the inadequate device, the viewing area and the image size of the CGH is not suitable for practical use.
Therefore, to reduce the required spatial frequency for the fringe pattern of the CGH, the position of the object is placed at the behind of the hologram plane.
Also, the huge calculation amount of the fringe pattern is big problem.
In our resent work, since we have developed our output device (named fringe printer) for the fringe pattern, the pixel pitch of the printed fringe pattern is improved from 0.87 &mu;m to 0.44 &mu;m.
By using the fringe printer, we have achieved to write over 100 Gpixel hologram.
Therefore, we investigate to make the floating image display with the fringe printer.
To realize the wider and larger image display, the image is reconstructed by the conjugate of the original reference wave to reproduce the real image.
Also, to solve the huge calculation amount, we employ the graphics processing unit to make calculation faster.

A liquid crystal panel for a video projector is often used for holographic television. However, its pixel size and pixel number are not enough for practical holographic 3-D display. Therefore, a multipanel configuration is generally used to increase the viewing window and displayed image size, and many spatial light modulators should be used in them. We propose a novel method to increase the viewing window of a holographic display system. The proposed method, which is implemented by using a mirror module and 4-f lens set, is to reconfigure the beam shape reflected by a spatial light modulator. The equipment is applied to a holographic display system, which has only a single spatial light modulator; a hologram could be displayed in a wider viewing window by the equipment than that of the conventional method. By the proposed method, the resolution of the reconfigured spatial light modulator has double resolution in the horizontal direction. Inversely, the vertical resolution is decreased. Even if the vertical resolution is decreased, a viewer could get 3-D effect because humans get more 3-D information in the horizontal direction. We have experimented using a liquid crystal on silicon (LcOS), whose resolution is 4096×2160 pixels. The reconfigured resolution by the mirror module is 8192×1080 pixels. From the experiments, the horizontal viewing window is almost two times wider than that without the mirror module. As a result, the hologram can be observed binocularly.

We investigate the computer-generated cylindrical rainbow hologram. Since the general flat format hologram has a limited viewable area, we usually cannot see the other side of the reconstructed object. There are some holograms to solve this problem. A cylindrical-type hologram is well known as the 360-deg viewable hologram. There are two kinds of cylindrical holograms, a multiplex hologram and a laser reconstruction 360-deg hologram. Since the multiplex hologram consists of many 2-D pictures, the reconstructed image is not truly 3-D. In contrast, a laser reconstruction 360-deg hologram has a true 3-D effect. However, since the spatial resolution of the output device is not enough and the calculation amount is huge, there are few reports on computer-generated cylindrical holograms. In our previous study, the computer-generated cylindrical hologram was realized as a Fresnel hologram. The calculation amount was too huge and took about 44 h in total calculation time, though we had used several PCs. We now propose the rainbow-type computer-generated cylindrical hologram. To decrease the calculation amount, the rainbow hologram sacrifices the vertical parallax. Also, this hologram can reconstruct an image with white light. Compared with the previous study of the Fresnel type, the calculation speed becomes 165 times faster. After calculation, we print this hologram with a fringe printer, and evaluate reconstructed images.

This report presents the results of computer simulation images for image-type Computer-Generated
Holograms (CGHs) observable under white light fabricated with an electron beam lithography system. The simulated
image is obtained by calculating wavelength and intensity of diffracted light traveling toward the viewing point from the
CGH. Wavelength and intensity of the diffracted light are calculated using FFT image generated from interference fringe
data. Parallax image of CGH corresponding to the viewing point can be easily obtained using this simulation method.
Simulated image from interference fringe data was compared with reconstructed image of real CGH with an Electron
Beam (EB) lithography system. According to the result, the simulated image resembled the reconstructed image of the
CGH closely in shape, parallax, coloring and shade. And, in accordance with the shape of the light sources the simulated
images which were changed in chroma saturation and blur by using two kinds of simulations: the several light sources
method and smoothing method. In addition, as the applications of the CGH, full-color CGH and CGH with multiple
images were simulated. The result was that the simulated images of those CGHs closely resembled the reconstructed
image of real CGHs.

A cylindrical hologram is well known to be viewable in 360 deg. This hologram depends high pixel resolution.Therefore, Computer-Generated Cylindrical Hologram (CGCH) requires huge calculation amount.In our previous research, we used look-up table method for fast calculation with Intel Pentium4 2.8 GHz.It took 480 hours to calculate high resolution CGCH (504,000 x 63,000 pixels and the average number of object points are 27,000).To improve quality of CGCH reconstructed image, fringe pattern requires higher spatial frequency and resolution.Therefore, to increase the calculation speed, we have to change the calculation method.
In this paper, to reduce the calculation time of CGCH (912,000 x 108,000 pixels), we employ Graphics Processing Unit (GPU).It took 4,406 hours to calculate high resolution CGCH on Xeon 3.4 GHz.Since GPU has many streaming processors and a parallel processing structure, GPU works as the high performance parallel processor.In addition, GPU gives max performance to 2 dimensional data and streaming data.Recently, GPU can be utilized for the general purpose (GPGPU).For example, NVIDIA's GeForce7 series became a programmable processor with Cg programming language.Next GeForce8 series have CUDA as software development kit made by NVIDIA.Theoretically, calculation ability of GPU is announced as 500 GFLOPS.
From the experimental result, we have achieved that 47 times faster calculation compared with our previous work which used CPU.Therefore, CGCH can be generated in 95 hours.So, total time is 110 hours to calculate and print the CGCH.

We have been investigating the computer-generated disk hologram (CGDH).
Since general flat format hologram has the limited viewable area, we usually cannot see the other side of the reconstructed object.
Therefore, we proposed the computer-generated cylindrical hologram (CGCH) to realize the 360 degrees viewable hologram.
However, the CGCH has the special shape, it is difficult to construct the CGCH and the calculation amount is too large.
In contrast, a disk type hologram is also well known as the 360 degrees viewable hologram.
Since the disk hologram is the reflective type flat hologram, the setup of reconstruction is very easy.
However, there was few report of the disk hologram by the computer-generated hologram.
Due to the lack of the spatial resolution of our output device, the hologram cannot provide the large diffraction angle.
In addition, the viewing zone is depended on the hologram size (of course, the maximum size of the fringe pattern is decided on the special frequency of the out put device), the calculation amount is also large (calculation amount of the CGDH is about quarter of the CGCH).
In our previous study, the computer-generated disk hologram was realized.
However, since the relation between the vertical viewing zone and reconstructed image size is trade-off, the size of the reconstructed image and view zone is not enough for practical use.
Therefore, to improve both parameters, we modified the fringe printer to output the high resolution fringe pattern for the disk hologram.

In this paper, we have investigated the computer-generated cylindrical rainbow hologram.
Since general flat format hologram has the limited viewable area, we usually can not see the other side of the reconstructed object.
There are some holograms to solve this problem.
A cylindrical type hologram is well known as the 360 degrees viewable hologram.
As the cylindrical holograms, there are two methods such as a multiplex hologram and a laser reconstruction 360 degrees hologram.
Since the multiplex hologram consists of the many two-dimensional pictures, the reconstructed image is not the true three-dimension.
In constant, a laser reconstruction 360 degrees hologram has the true three-dimensional effect.
However, since the spatial resolution of the output device is not enough and the huge calculation amount, there are few reports on computer-generated cylindrical hologram.
In our previous study, the computer-generated cylindrical hologram was realized as the Fresnel hologram.
The calculation amount was too huge and took about 44 hours in the total calculation time, though we had used the several PCs.
We propose the rainbow type computer-generated cylindrical hologram.
To decrease the calculation amount, the rainbow hologram sacrifices the vertical parallax.
Also, this hologram can reconstruct the image with white light.
Comparison with the previous study of the Fresnel hologram, the calculation speed becomes 165 times faster.
After the calculation, we print this hologram with the fringe printer, and evaluate reconstructed images.

A liquid crystal panel is often used for holographic television.
However, its pixel size and pixel number are not enough for practical holographic 3D display.
Therefore, multi-panel configuration is often used to increase the viewing angle and displayed image size.
However, many spatial light modulators should be used in them. In this paper, we propose a novel method to increase the viewing angle of a holographic display system.
The proposed method, which is implemented by a mirror module, is to reconfigure the beam shape reflected by a spatial light modulator.
In this paper, the equipment is applied to a holographic display system, which has only a single spatial light modulator and can display a hologram in wider viewing angle than that of the conventional method.
By the proposed method, the resolution of the reconfigured spatial light modulator has double resolution in horizontal direction.
Inversely, the vertical resolution is decreased because the human get more 3D information in horizontal direction.
We have experimented using a Liquid Crystal on Silicon, whose resolution is 4,096 x 2,160 pixels.
And the reconfigured resolution by the mirror module is 8,192 x 1,080 pixels.
From the experimental results, the horizontal viewing angle is almost two times wider than that of the conventional method without the mirror module.
We have achieved that the hologram can be observed binocularly.

For practical holographic video display, it is important to generate holographic fringes as fast as possible. It is also important to display the full-color image with a simple display system. In our previous study, a full-color hologram was realized as a rainbow hologram, which discards the vertical parallax to reduce computation complexity. Its color reproduction, however, is not enough. Since this hologram uses the horizontal slit, proper color reproduction can be obtained only from a narrow viewing area in the vertical direction. In contrast, the image hologram provided a good contrast image, although it had only a single color. Also, the image hologram has full-parallax information. In this work, we investigate the image hologram for fast calculation and the display optics for full-color holograms with full parallax. Since image points are located close to the hologram, the required computation area of the image hologram becomes much smaller than that of the entire hologram. Therefore, vastly improved computational speed is obtained. The full-color hologram is displayed on a holographic video display system, which uses part of the original optics and liquid crystal on silicon (LCoS) panels of the conventional video projector to separate and combine color components. From the experimental results, we obtain a full-parallax reconstructed image and better color reproduction compared with the rainbow hologram.

A common difficulty in displaying a Fresnel hologram in real time the required calculation of huge amounts of information. We propose a novel digital hologram generation method for real-time holographic display. It depends on compensation of the phase-added stereogram, and can generate high-quality holograms rapidly. We describe a generation algorithm for the phase-added stereogram, using the fast Fourier transform (FFT) for fast calculation, and the compensated phase-added stereogram to get a reconstructed image as clear as the Fresnel hologram. Moreover, we present a method to define the optimum size of segmentation to get a clear reconstruction image and to achieve fast computation using the FFT. We have built a demonstration system to implement the proposed method. The system consists of a server, a client, and an optical holographic display system for real-time holographic display. The server generates 3-D information and transmits it on Ethernet. The client receives the information and generates a digital hologram using the compensated phase-added stereogram. Finally, the generated hologram is displayed on the optical holographic display system in real time. We have achieved display of digital holograms at 15 frames/s with 1000 object points.

A typical difficulty to display the Fresnel hologram in real time is calculation of huge information. In this paper,
we propose a method to define the optimum size of segmentation for the Phase-Added Stereogram, which can
generate high quality hologram rapidly, and describe a generation algorithm of the Phase-Added Stereogram
using the Fast-Fourier Transform for fast calculation. Moreover, we have built an optical holographic display
system for real-time holographic display to implement the proposed method. To generate the fringe pattern,
we used 3D information, which is a set of the 3D points converted from a 3D model. Finally, the generated
hologram is displayed on the optical holographic display system in real time. In consequence, we could achieved
that digital hologram can be displayed at 15 frame/second with 1,000 object points.

In this paper, we have investigated real time calculation and display optics of full color hologram with full parallax. In our previous study, full color hologram was realized as the rainbow hologram which discards vertical parallax to reduce computation complexity. Since the color of the reconstructed image changes when observer moves to the vertical direction even a little, proper color reproduction can be obtained only from narrow viewing area. And this hologram has horizontal parallax only.
In this study, we employ the image hologram for better color reproduction and full parallax reconstruction. When we calculate the image hologram, we use the virtual window to reduce the calculation amount. By using the virtual window, we could achieve 253 times faster the calculation speed compare with Fresnel hologram using the difference method. The full color hologram is displayed on the holographic television (HoloTV), which uses a part of original optics and LCoS panels of the conventional video projector (Cannon POWERPROJECTOR SX50) to separate and combine color components.
From experimental results, computational speed of the full-color image hologram is almost same as the full-color rainbow hologram and color reproduction is better than that of the rainbow hologram. We also could achieve to reconstruct good quality animation.

For practical holographic video system, it is important to generated holographic fringe as fast as possible. We have proposed an approximation method that can calculate the hologram faster. However, for the full parallax Fresnel hologram, the speed is not enough for real-time calculation. In this paper, we change the type of hologram from Fresnel to image. Since the object points of the image hologram are located very close to the hologram, calculations for single object point require only fractional part of the hologram. This also makes computation quite fast. The image hologram with 1.47 million pixels hologram, the speed of ten frames per second is obtained with the object consists of 7,000 points. Experimental results demonstrate that the interactive computation of complex object can be generated with conventional PC. We also investigated rainbow hologram for both full-color reconstruction and fast calculation. Reconstructed image prove that the color registration is good thorough the view zone. From the experimental results, compared with the image hologram, we could achieve about two times calculation speed when the number of the object point is more than 17,000. This results demonstrate that the interactive computation of full-color object can be generated
with conventional PC.

It becomes quite easy to calculate over one hundred million pixels computer-generated hologram of three-dimensional object, even with normal personal computers. On the other hand, it is not so easy to output the calculated result as a hologram that must have micron order resolution for practical three-dimensional display. We have developed a direct fringe printer, which consists of a laser, an X-Y stage and a liquid crystal panel as a spatial light modulator. A fractional part of the entire holographic fringe is displayed on the liquid crystal panel, and the demagnified image of it is recorded on a holographic plate. Then the plate is translated by the x-y stage to write next part of the fringe. We have made some improvements on our previous system. We achieved to print 192 Mega-pixel hologram with 2.8-micron pitch within 40 minutes, three times faster than the previous one. We have also printed 768 Mega-pixel hologram and the full-color rainbow hologram.

It becomes quite easy to calculate over one hundred million pixels computer-generated hologram of three
dimensional objects, even with normal personal computers. On the other hand, it is not so easy to output the
calculated result as a hologram that must have micron order resolution for practical three dimensional displays.
It is possible to use the electron beam writer and the laser plotter, which are used to make masks for integrated
circuits. However, these equipments are quite expensive and not suitable for personal use. There have been
reported some results of compact and inexpensive direct fringe printing. They use a laser and an x-y stage,
and the fringe pattern is written point by point, which takes very long time. We are developing area by area
writing printer, which consists of the laser, the x-y stage and a liquid crystal panel as a spatial light modulator.
A fractional part of the entire holographic fringe is displayed on the liquid crystal panel, and the demagnified
image of it is recorded on a holographic plate. Then the plate is translated by the x-y stage to write next part
of the fringe. The system configuration and preliminary results are described.

We have reported that viewing angle of the computer-generated hologram can be expanded with lensless Fourier transform hologram. It, however, requires a laser to illuminate the CGH for reconstruction. In the previous paper, we have proposed that making the second hologram for white-light reconstruction. The reconstructed image from the first hologram is used as the object beam of the second hologram. The second hologram can be either transmission or reflection hologram, which depends on the direction of the reference beam. In this report, we extend this method to make multi-color reflection hologram. First, we calculate the master holograms for each elemental color. Then, the transfer hologram can be made from the master CGH with multimple exposure with either changing wavelength or psuedo-color process. In the experimental result, we obtain multi-color full-parallax computer-generated hologram with 20 degrees of viewing angle and 10 mm × 7.6 mm image size.

We have reported that viewing angle of the computer- generated hologram can be expanded with lensless Fourier transform hologram. It however, requires a laser to illuminate the CGH for reconstruction. In the previous paper, we have proposed that making the second hologram for white-light reconstruction. The reconstructed image from the first hologram is used as the object beam of the second hologram. The second hologram can be either transmission or reflection hologram, which depends on the direction of the reference beam. In this report, we extend this method to make the full-parallax computer-generated holographic stereogram. At first, we calculate the master hologram consists of elementary holograms. Each elementary hologram is calculate by Fast Fourier Transform of perspective 2D image. Then, the transfer hologram can be made from the master CGH with single exposure. In the experimental result, we obtain full-parallax computer-generated holographic stereogram with 20 degrees of viewing angle and 10 mm X 7.6 mm image size.

The viewing angle of the computer-generated hologram (CGH) can be expanded with lens-less Fourier configuration. It, however, requires a laser to illuminate the CGH for reconstruction. In the previous paper, we have proposed that making the second hologram for white-light reconstruction. The reconstructed image from the first hologram is used as the object beam of the second hologram. The second hologram can be either transmission or reflection hologram, which depends on the direction of the reference beam. In this paper, we propose a method to calculate CGH for the full- color rainbow hologram with enlarged viewing angle. First, we calculate the master hologram with three virtual slits whose positions are corresponding to red, green and blue wavelength. The transfer hologram can be made from the master CGH with single exposure. In the experimental result, we obtain full-color computer-generated rainbow hologram with 17 degrees of viewing angle and 3.0 mm by 2.5 mm image size.

For practical holographic video system, it is important to generated holographic fringe as fast as possible. We have proposed an approximation method that can calculate the Fresnel hologram fast. To compute the hologram, an object is assumed as a collection of self-illuminated points and the fringes from each object point are superposed. To determine the fringe, a distance between object point and sampling point on the hologram is used to obtain phase of the light. Since sampled hologram usually has small pixel intervals, the difference of the distance values between adjacent pixels is also small and its n-th order difference becomes a constant. Therefore, the distance value at certain pixel can be obtained from the neighbor pixel with simple additions. We have investigated approximation errors and computational speed of the method. The numerical results show that the proposed method is quite effective. The distance error can be reduced less that one wavelength with practical parameters and the computational speed becomes 16 times faster than conventional method. With the proposed method, a hologram, which has horizontal parallax only, 1.3 mega- pixels and 1,000 object points, can be calculated less than on second with a personal computer.

We investigate the use of lens-less Fourier hologram to enlarge viewing angle of the computer-generated holograms (CGH) whose resolution is relatively low such as a photographic reduction. For image reconstruction, this hologram requires the point illumination source near the hologram. To avoid the use of such special illumination, we made secondary hologram with collimated reference beam and the reconstructed beam of the CGH. The second hologram has wide viewing angle and can be reconstructed with collimated white-light illumination.

In this report, computer-generated holograms (CGH's) which have the ability to reconstruct multi-level 3-D images under white light are described. For trial fabrication of the CGH, an electron beam printing system (EBPS) which is capable of recording interferogram data (IFD) with submicron precision is utilized. Because EBPS is controlled with on-off switching, IFD needs to be transformed into minute rectangle cells with their locations corresponding to the fringe. In our previous report, the intensity of the IFD was quantized into 2 levels with the median threshold, and then transformed into the cells. By this method, the location information of the IFD can be retained, while the intensity information, which is essential to reconstruct the tone of images, cannot. To solve this problem, pulse-width modulation (PWM), in which the intensity is quantized into multi levels is used, then the cell width is determined in proportion to the quantized intensity value, and applied to the IFD transformation. As a result of this experiment, in which 8 leveled PWM is applied to the IFD transformation, a 7 level-shaded pyramid is found to be sufficient, and therefore the effectiveness of the transforming method for reconstructing multi-level 3-D images has been confirmed experimentally.

Trial fabrication of image-type CGHs which are recorded by an electron beam printing system to display 3D images is described. First, to verify the feasibility of fabricating CGHs for 3D image reconstruction, two preliminary experiments, in which the divergence of the object wave was limited in one horizontal plane and the reference wave was defined as a plane wave from the horizontal direction, were performed. To confirm that the depth of reconstructed images can be perceived, two flat images (characters G and R) differing in depth and a simple wire frame object including some lines in the depth direction, were selected as object data. Both images were successfully reconstructed under the white light and thus the feasibility has been supported experimentally. Secondly, to reduce the blur caused by chromatic aberration and to improve the uniformity in luminous intensity in the reconstructed G-R image, the CGH was modified to image-type and the angle of divergence of the object wave was narrowed; thus the reconstructed image has been improved. Finally, to facilitate observation of the reconstructed image, the direction of the reference wave was modified to the vertical direction. All of the reconstructed images are shown and some technical problems are also mentioned.

Hologram-like video images have been demonstrated using a stereoscopic display developed by a member of the 3-D project at TAO. Images are made of 45-view stereoscopic images at resolution of 400 by 400 pixels -- each pixel has 45 horizontal parallaxes -- and refreshed at 30 Hz. Stimulation of conventional stereoscopic video display causes a physiological problem, called accommodation-vergence conflict, though it provides multi-view images. Holography is a usual approach to avoid this conflict but it has great difficulty of providing video images. A new stereoscopic approach is described in this paper, called super multi-view (SMV) region. SMV region means the following condition; there are more than two parallax-images passing through a pupil of viewer's each eye. At the SMV region, if viewer accommodates one's focus to the spatial position of 3-D image -- perceived by binocular disparity -- then the parallax-images passed through a pupil are focused to the same position on a retina. Therefore, there is an ability of fusing accommodation and vergence due to the effect of monocular and binocular parallax. To satisfy the SMV condition, the display must provide numerous view images with narrow interval of parallax. It is difficult to satisfy the SMV condition using conventional displaying technique, but the FLA concept (proposed at Practical Holography X, EI '96) realized providing 45-view images with 0.5 degree interval. The design of this display is also described in this paper. SMV technique is just a quasi-holography because reproduced images have natural stimulus for monocular and binocular vision.

High-speed calculation of hologram is very important to realize the continuous real-time holographic 3D-TV. We are studying computer systems and algorithms for the high-speed calculation of hologram. We have proposed three high-speed calculation systems of Fresnel-hologram. But, they didn't come up to real-time holographic 3D-TV when the object is complex. In this paper we have proposed holographic-stereogram calculation system using the graphic-accelerator and the digital-signal-processor (DSP) system. Holographic-stereogram calculation time doesn't depend on complexity of the object. A fast-Fourier-transform of object is calculated fast using the DSP system. We make clear that the continuous real-time holographic 3D-TV will be realized in the near future.

We propose a simplified model to calculate the computer generated rainbow hologram fast. The rainbow hologram is very practical to display 3D images because the images can be reconstructed by white light. Since the rainbow hologram has horizontal parallax only, less computation is required compared with full parallax transmission holograms. In the proposed method, we can simply generate the final hologram from intermediate data, whose total number of samples can be less than one tenth of the final hologram. This intermediate format makes fast computation and effective storage/transmission possible. It can be done only multiple and additional operation to convert the intermediate data to the final data. Therefore, it is possible that a hardware implementation to the electro-holographic display or printer. In this paper, we discuss both theory for the simplified model and experimental results of white light reconstructed images. Full color holograms are also discussed.

We have demonstrated that 2D motion picture coding technique can be used effectively to compress the holographic fringe pattern. It is not practical to apply 2D image compression directly to the hologram because the character of the holographic fringe data is quite different from that of normal 2D images. Before the compression, we segment and transform hologram to obtain local spatial frequency spectra of the holographic fringe. These segmented spectra of the hologram become similar to a series of perspective images of the object taken by laterally moving camera. Therefore, 2D moving image compression technique, such as MPEG, can be used. Since the compression rates and image quality depend on the segmentation size and MPEG parameters, we seek the optimum condition to obtain high compression rate with small affect on image quality. We will also discuss experimental results of the relation between compression rates and image quality obtained by the proposed methods.

The performance of an electro-holographic display has been limited by space and spatial bandwidth of spatial light modulators. This paper presents a new type 3D display using numerous small-size light sources. The concept of the display is based on the electro- holographic display using acousto-optic devices. Each light source is aligned on a circle at narrow intervals, and its output beam is focused on the center of the circle. Its focal point or the image of its focal point is scanned by the mechanical X-Y scanner, and each light's intensity is modulated by each parallax image of the viewing angle. This display can produce big-and-natural 3D images with high resolution and high refresh-rate.

To realize an interactive holographic 3D display system, the system falls into three processes: the first is the generation of original 3D object data; the second is the computation of hologram patterns; the third is the modulation of electro-holographic display devices. These must be executed fast and continuously for 3D display. In these processes, the fast computation of holograms is the most important process. We investigate this process using a fast computation algorithm with a fast computing system, and fabricated a prototype of the interactive holographic 3D display system. We discuss the fast computation algorithm using a transform from frequency domain to spatial domain compared with the traditional computation method of the Fresnel hologram, reduction of calculation time using our fast computing system.

We propose parallel architecture, which consists of small display units, to make up a large electro-holographic display. It is difficult to make a large 3D display using electro-holography because it requires a lot of calculations, broad bandwidth, and restrictions of optical and mechanical elements. In this paper, we discuss the problems, then show basic idea of architecture and preliminary experimental results.

The holographic stereogram approach is used to reduce computational time of computer- generated hologram for 3D displays. It can be obtained by Fourier transforms of an array of 2D perspective images, and computational speed is quite faster than that of Fresnel hologram. However, the conventional holographic stereograms are made from an array of pure 2D perspective images, which do not have depth information. Therefore, the reconstructed 3D image has lower resolution than that of Fresnel hologram. In this paper, we have discussed the stereographic approach as an approximation of wavefront reconstruction, and propose `integral hologram' which can be defined as an improved or `coherent' stereogram. `Integral hologram' is calculated by a similar way to the holographic stereogram. However, the input data are obtained not from an array of 2D perspective images, but from 3D coordinates of the object. From numerical analysis, we demonstrate that the `integral hologram' has image resolution as high as Fresnel hologram, and can be computed as fast as the conventional holographic stereogram.

A 2D image can be scaled simply by changing its pixel size. If we were to apply this model to a hologram, it would cause distortion in the reconstructed 3D images, and a change in the viewing angle. We propose a method for scaling the reconstruction image without changing its fringe element, i.e., pixel size. We divide the hologram into small blocks. Then, these blocks are repositioned in order to magnify or demagnify the reconstructed image. This method maintains the viewing angle and causes no distortion. It does, however, blur the reconstructed image. To reduce the blur, we propose a method of interpolation in the frequency domain. Results of experiments performed on an electro-holography system are also presented.

Because the information content of a hologram is extraordinarily large, information reduction is essential to the realization of a practical electro-holographic display system. We have investigated a sub-sampling method to reduce the information content of an electro- holographic display. This sub-sampling, however, also causes a blurring of the displayed 3D images. We discuss both the theory of the relation between the information reduction rate and the image blur and our experimental results.

Recently, a real-time holographic display system has been developed at MIT. The system can generate, transmit, and display holographic images in real-time. Although the display device itself can treat tens of images in a second, computational time to generate holographic fringe pattern takes a second to a few seconds even on a supercomputer. In this paper, holographic stereogram approaches to reduce its computational time are studied. Basic experimental results are also discussed.

Any practical holographic display device relying on the MIT synthetic aperture approach will require time-bandwidth products far exceeding those available with single channel acousto- optic modulators (AOMs). A solution to this problem is to use a multichannel AOM, thus making use of the parallelism inherent in optical systems. It is now technically feasible to accommodate a large number of acoustic channels on a single crystal with a corresponding improvement in image characteristics. The vertical view zone also becomes a significant problem for any large size display since each horizontal scan line is visible only from a narrow angle in the vertical direction. Using holographic optical elements (HOEs) alleviates this limitation in two ways: First, the interline spacing can be adjusted easily with HOEs. Second, it is possible to manufacture an HOE which will act as a one-dimensional diffuser. Placing such an HOE in the vertical focus plane of the display increases the view zone by diffusing each line in the vertical direction, but leaves the horizontal image content unaltered.

High-power glass laser systems for laser fusion use many BK-i glasses and the laser-induced damage of this glass is a serious problem. Since the BK-i glass is generally melted in platinum (Pt) crucibles the laser damage due to metallic Pt particles occurs inside the glass. The Pt particles cause fractures when irradiated at a fluence higher than 3 J/cm with 1064 nm 15 ns laser pulse. The size of the fracture increases with irradiation fluence and the damaged glass has to be replaced. In special cases BK-i glass is melted in ceramic crucibles but there is a problem of cristobalite production inside the BK-i glass. The laser damage threshold of cristobalite is about 4. 5-5. 5 JIcm with 1064 nni 15 ns laser pulse. We have found average damaged particles in BK-i glasses melted in Pt and ceramic crucibles to be 200-400 and 10 particles per liter respectively. At present laser damage in BK-i glass is being improved by changing a composition ratio of melting materials.

We present an electro-optical apparatus capable of displaying a computer generated hologram
(CGH) in real time. The CGH is calculated by a supercomputer, read from a fast frame buffer, and
transmitted to a high-bandwidth acousto-optic modulator (AOM). Coherent light is modulated by the
AOM and optically processed to produce a three-dimensional image with horizontal parallax.

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